In 1906 the great San Francisco earthquake and fire destroyed much of the city. As we approach the 100-year anniversary of that event, a critical concern is the hazard posed by another such earthquake. In this article, we examine the assumptions presently used to compute the probability of occurrence of these earthquakes. We also present the results of a numerical simulation of interacting faults on the San Andreas system. Called Virtual California, this simulation can be used to compute the times, locations, and magnitudes of simulated earthquakes on the San Andreas fault in the vicinity of San Francisco. Of particular importance are results for the statistical distribution of recurrence times between great earthquakes, results that are difficult or impossible to obtain from a purely field-based approach.